Energy minimizing harmonic maps with an obstacle at the free boundary

Duzaar F, Grotowski JF (1994)

Publication Type: Journal article

Publication year: 1994

Journal

Manuscripta Mathematica Springer Verlag (Germany)

Publisher: Springer Verlag (Germany)

Book Volume: 83

Pages Range: 291-314

Journal Issue: 34

URI: http://www.springerlink.com/content/m67p822218012813/fulltext.pdf

DOI: 10.1007/BF02567615

Abstract

We consider partial regularity for energy minimizing maps satisfying a partially free boundary condition. This condition takes the form of the requirement that a relatively open subset of the boundary of the domain manifold be mapped into a closed submanifold with non-empty boundary, contained in the target manifold. We obtain an optimal estimate on the Hausdorff dimension of the singular set of such a map. Our result can be interpreted as regularity result for a vector-valued Signorini, or thin-obstacle, problem.

Authors with CRIS profile

Frank Duzaar

Involved external institutions

Rheinische Friedrich-Wilhelms-Universität Bonn DE Germany (DE) Universität des Saarlandes (UdS) DE Germany (DE)

How to cite

APA:

Duzaar, F., & Grotowski, J.F. (1994). Energy minimizing harmonic maps with an obstacle at the free boundary. Manuscripta Mathematica, 83(34), 291-314. https://dx.doi.org/10.1007/BF02567615

MLA:

Duzaar, Frank, and Joseph F. Grotowski. "Energy minimizing harmonic maps with an obstacle at the free boundary." Manuscripta Mathematica 83.34 (1994): 291-314.

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